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We present a logic, called Relational Higher Order Logic (RHOL), for proving relational properties of a simply typed λ-calculus with inductive types and recursive definitions. ... proofs in higher-order logic. ... ACKNOWLEDGMENTS We thank the anonymous reviewers for their helpful and thoughtful comments. This article is based on research that has been supported, in part, by NSF under grant TWC-1565365. ...doi:10.1145/3110265 dblp:journals/pacmpl/AguirreBG0S17 fatcat:tt2j2f4lqvgjpmtya2lpkhqi7m
We present a logic, called Relational Higher Order Logic (RHOL), for proving relational properties of a simply typed λ-calculus with inductive types and recursive definitions. ... In a higher-order setting, relational program verification can be achieved using relational refinement type systems, a form of refinement types where assertions have a relational interpretation. ... A relational modal logic for higher-order stateful ADTs. ...arXiv:1703.05042v1 fatcat:o6w2un7m3zfrndpj2lagsc7zom
We present a logic, called relational higher-order logic (RHOL), for proving relational properties of a simply typed λ-calculus with inductive types and recursive definitions. ... In a higher-order setting, relational program verification can be achieved using relational refinement type systems, a form of refinement types where assertions have a relational interpretation. ... A relational modal logic for higher-order stateful ADTs. ...doi:10.1017/s0956796819000145 fatcat:yxlwrfjjevgpxmo5ulbie5gsn4
data types Logical relations Local state Parametricity We present a realizability model for reasoning about contextual equivalence of higher-order programs with impredicative polymorphism, recursive types ... , and higher-order mutable state. ... And we thank the anonymous referees for many valuable comments, ranging from typos to directions for future work. ...doi:10.1016/j.jlap.2012.03.004 fatcat:laxrygwefvffjfllvckzobxydu
Constraints in Computational Logics
The -calculus provides for higherorder relational programming with rst-order constraints, and subsumes higher-order functional programming as a special case. ... The -calculus provides for logical variables but not for rst-order uni cation, which would amount to the integration of a tree constraint system. ... Introduction We present the -calculus, a relational calculus parametrized by a logical constraint system. The -calculus provides for higher-order relational programming with rst-order constraints. ...doi:10.1007/bfb0016846 dblp:conf/ccl/NiehrenS94 fatcat:uuy6athywvba5koluxdrvvmy7q
Higher-Order Separation Logics Instead of specifying a program by relating it to another program, we can specify programs using program logics. ... I will consider both relational models and program logics based on higher-order separation logic. ...doi:10.1145/2535838.2537849 dblp:conf/popl/Birkedal14 fatcat:hjgtj3khsfg2zk766px2gexvaq
From the introduction: “In this chapter, we develop the idea of higher-order logic programming by utilizing a higher-order logic as the basis for computing. ... There are, of course, many choices for the higher-order logic that might be used in such a study. ...
It covers syntax, semantics, and pragmatics of higher-order logic programming in a systematic and easy-to-read manner that will be of great value as introduction and reference for students and researchers ... This book is concerned with the second form when the underlying logic is higher-order logic. ... Much has happened since the initial development of higher-order logic programming. Andreoli discovered the general theory of focusing as a broad basis for logic programming. ...doi:10.1017/s1471068414000027 fatcat:fh5pyehajzazjm6ynvgvc6ojlq
Lecture Notes in Computer Science
Are higher-order extensions to logic programming needed? We answer this question in the negative by showing that higher-order features are already available in pure logic programming. ... It is demonstrated that higher-order lambda calculus-based languages can be compositionally embedded in logic programming languages preserving their semantics and abstraction facilities. ... The objective here seems to be not higher-order logic programming, but logic programming over higher-order terms. ...doi:10.1007/3-540-58025-5_63 fatcat:qdq44baxdzfudg3ieh47p62344
Automated Mathematical Induction
We propose a novel approach to automating the synthesis of logic programs: Logic programs are synthesized as a by-product of the planning of a veri cation proof. ... The approach is a two-level one: At the object level, we prove program veri cation conjectures in a sorted, rst-order theory. The conjectures are of the form 8args ????! : prog(args ????! ... Thus, what we do is closely related to proving the higher-order conjecture 9P: 8args ????! : P(args ????! ) $ spec(args ????! ) where P represents a pure logic program. ...doi:10.1007/978-94-009-1675-3_4 fatcat:hlrfxol3oreppivyqvd5k7rzyy
The authors present four abstract programming languages: first- order and higher-order positive Horn clauses, and first-order and higher-order versions of a new class of formulas called hereditary Harrop ... For example, first-order Horn clauses do not support modules, abstract data types or higher-order functions. ...
Every stratgied program computes a Ai relation on N = (N, +, . ). As a result, fixpoint logic has strictly higher expressive power than stratified logic programs on the integers. ... Fixpoint logic has higher expressive power than stratified logic programs on finite structures over any vocabulary that has a relational symbol of arity at least two. ...doi:10.1016/0890-5401(91)90059-b fatcat:aexvileko5f55b2uvolbkueynu
Both languages are based on a higher-order functional language. The relevance of higher-order features in logic languages will be discussed in Section 10. ... On the other hand, lazy evaluation is highly desirable, mainly in a functional-relational logic language, in order to define nonstrict functions (and relations) and for stream-based logic programming. ... Let us finally remark that higher-order features could play a very important role in logic programs, in addition to what is relevant to programming in general. ...doi:10.1016/0743-1066(86)90014-2 fatcat:kzu7tvyz2fajvlsl767fgczjfe
Motivated by applications in automated verification of higher-order functional programs, we develop a notion of constrained Horn clauses in higher-order logic and a decision problem concerning their satisfiability ... Following work in higher-order program verification, we develop a refinement type system in order to reason about and automate the search for models. ... Research was partially completed while the second and third authors were visiting the Institute for Mathematical Sciences, National University of Singapore in 2016. ...arXiv:1705.06216v2 fatcat:qc4rib7saragnbcnzshaxt4hpu
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